In the lattice semigroup the sl ideal set SL (S) is lattice, but the supremum of two sl ideals is not same as their union, all sl ideals are generated by the ideal in the general lattice semigroup.

• 在格半群中，sl理想集是格，但是2个sl理想的上确界不等于其并。广义格半群中的理想均能生成sl理想。